I'm a sort of newbie, I would like to know how and what the implications are of 'Generating a string of random standard normal variables that are correlated with each other'.
To get by this problem, I have been generating and correlating my desired sequence to a different random variable and then calculating the correlation between my sequence.
Thanks for the anticipated answer.
ps: Generate random standard normal's A, B, C, D so that have a correlation and standard deviation of corr and std.
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I am not sure if this is homework or not ...
Start off with two independent random variables with zero mean and standard deviation sigma.
sigma = 10; X = sigma*randn(1e7, 1); Y = sigma*randn(1e7, 1);
Then make two new random variables from these with correlation rho.
rho = 0.2; A = X; B = sqrt(rho^2)*X+sqrt(1-rho^2)*Y;
[std(A), std(B)] corrcoef(A, B)
When you add a third random variable C you need to specify what you want rho_AB, rho_AC, and rho_AB to be. The basic idea is the same: start with N independent random variables and add them together with appropriate weighting to get N new random variables.
Given a correlation matrix C = A*A', then A = P*sqrt(D), where:
[P,D] = eig(C); % spectral decomposition
To get the correlated normal random series Z, use W = (W1, ...,W2)' (the normal random series):
Z = A*W;
Note that if you have 4 variables, then C is 4 by 4, and W should be 4 by nobs.